Three solutions for some Dirichlet and Neumann nonlocal problems

Abstract

This article is concerned with a class of nonlocal Dirichlet and Neumann boundary-value problems depending on two real parameters. Our approach relies on variational methods: we establish the existence of three weak solutions via a recent abstract multiplicity result by Ricceri about nonlocal problems.

Keywords:

• variational method
• nonlocal problem
• boundary value problem

AMS Subject Classifications::

• 35A01
• 35A15

Acknowledgements

The authors wish to thank the anonymous referees for their careful reading of this article and their useful comments and suggestions which have improved the quality of this article.